Face recognition with combined PCA-based datasets

ABSTRACT

A representation framework is determined in a face recognition method for a first collection of facial images including at least principle component analysis (PCA) features. A representation of said first collection is stored using the representation framework. A modified representation framework is determined based on statistical properties of original facial image samples of a second collection of facial images and the stored representation of the first collection. The first and second collections are combined without using original facial image samples. A representation of the combined image collection (super-collection) is stored using the modified representation framework.

PRIORITY

This application is a Continuation of U.S. patent application Ser. No.12/418,987, filed Apr. 6, 2009, now U.S. Pat. No. 8,050,466; which is aContinuation of U.S. patent application Ser. No. 11/833,224, filed Aug.2, 2007, now U.S. Pat. No. 7,515,740; which claims the benefit ofpriority to U.S. provisional patent application Ser. No. 60/821,165,filed Aug. 2, 2006, which is hereby incorporated by reference.

BACKGROUND OF THE INVENTION

Face tracking technology has been recently introduced into consumerdigital cameras enabling a new generation of user tools for the analysisand management of image collections (see, e.g.,http://www.fotonation.com/index.php?module=company.news&id=39, whereinthe entire site www.fotoination.com is incorporated by reference. Inearlier research, it had been concluded that it should be practical toemploy face similarity measures as a useful tool for sorting andmanaging personal image collections (see, e.g., P. Corcoran, G.Costache, Automated sorting of consumer image collections using face andperipheral region image classifiers, Consumer Electronics, IEEETransactions on Volume 51, Issue 3, August 2005 Page(s):747-754; G.Costache, R. Mulryan, E. Steinberg, P. Corcoran, In-cameraperson-indexing of digital images Consumer Electronics, 2006, ICCE '06.2006 Digest of Technical Papers, International Conference on 7-11 Jan.2006 Page(s):2; and P. Corcoran, and G. Costache, Automatic System forIn-Camera Person Indexing of Digital Image Collections, ConferenceProceedings, GSPx 2006, Santa Clara, Calif., October 2006, which are allhereby incorporated by reference). The techniques described in thisresearch rely on the use of a reference image collection as a trainingset for PCA based analysis of face regions.

For example, it has been observed that when images are added to such acollection there is no immediate requirement for retraining of the PCAbasis vectors and that results remain self consistent as long as thenumber of new images added is not greater than, approximately 20% of thenumber in the original image collection. Conventional wisdom on PCAanalysis would suggest that as the number of new images added to acollection increases to certain percentage that it becomes necessary toretrain and obtain a new set of basis vectors.

This retraining process is both time consuming and also invalidates anystored PCA-based data from images that were previously analyzed. Itwould be far more efficient if we could find a means to transform faceregion data between different basis sets.

In addition, it has been suggested that it is possible to combinetraining data from two or more image collections to determine a commonset of basis vectors without a need to retrain from the original facedata. This approach has been developed from use of the “mean face” of animage collection to determine the variation between two different imagecollections.

The mean face is computed as the average face across the members of animage collection. Other faces are measured relative to the mean face.Initially, the mean face was used to measure how much an imagecollection had changed when new images were added to that collection. Ifmean face variation does not exceed more than a small percentage, it canbe assumed that there is no need to recompute the eigenvectors and tore-project the data into another eigenspace. If, however, the variationis significant between the two collections, then the basis vectors areinstead re-trained, and a new set of fundamental eigenvectors should beobtained. For a large image collection, this is both time consuming andinefficient as stored eigenface data is lost. It is thus desired to havean alternative approach to a complete retraining which is both effectiveand efficient.

SUMMARY OF THE INVENTION

A face recognition method for working with two or more collections offacial images is provided. A representation framework is determined fora first collection of facial images including at least principlecomponent analysis (PCA) features. A representation of said firstcollection is stored using the representation framework. A modifiedrepresentation framework is determined based on statistical propertiesof original facial image samples of a second collection of facial imagesand the stored representation of the first collection. The first andsecond collections are combined without using original facial imagesamples. A representation of the combined image collection(super-collection) is stored using the modified representationframework. A representation of a current facial image, determined interms of the modified representation framework, is compared with one ormore representations of facial images of the combined collection. Basedon the comparing, it is determined whether one or more of the facialimages within the combined collection matches the current facial image.

The first collection may be updated by combining the first collectionwith a third collection by adding one or more new data samples to thefirst collection, e.g., according the further face recognition methoddescribed below.

Data samples of the first collection may be re-projected into a neweigenspace without using original facial images of the first collection.The re-projecting may instead use existing PCA features.

Training data may be combined from the first and second collections.

The method may be performed without using original data samples of thefirst collection.

The first and second collections may contain samples of differentdimension. In this case, the method may include choosing a standard sizeof face region for the new collection, and re-sizing eigenvectors usinginterpolation to the standard size. The samples of different dimensionmay be analyzed using different standard sizes of face region.

The modified representation framework may be generated in accordancewith the following:

${C\hat{o}v_{C}} = {{\frac{N^{C\; 1}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 1} \times {\hat{V}}^{C\; 1} \times {\hat{E}}^{C\; 1^{T}}} \right\rbrack} + {\frac{N^{C\; 2}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 2} \times {\hat{V}}^{C\; 2} \times {\hat{E}}^{C\; 2^{T}}} \right\rbrack} + {{\frac{N^{C\; 1}N^{C\; 2}}{\left( {N^{C\; 1} + N^{C\; 2}} \right)^{2}}\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack} \times \left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}}}$

A further face recognition method for working with two or morecollections of facial images is also provided. Different representationframeworks are determined for first and second collections of facialimages each including at least principle component analysis (PCA)features. Different representations of the first and second collectionsare stored using the different representation frameworks. A modifiedrepresentation framework is determined based on the differentrepresentations of the first and second collections, respectively. Thefirst and second collections are combined without using original facialimage samples. A representation of the combined image collection(super-collection) is stored using the modified representationframework. A representation of a current facial image, determined interms of the modified representation framework, is compared with one ormore representations of facial images of the combined collection. Basedon the comparing, it is determined whether one or more of the facialimages within the combined collection matches the current facial image.

The PCA features may be updated based on first eigenvectors and firstsets of eigenvalues for each of the first and second collections. Theupdating may include calculating a new set of eigenvectors from thepreviously calculated first eigenvectors of the first and secondcollections.

The method may be performed without using original data samples of thefirst and second collections.

The first and second collections may contain samples of differentdimension. A standard size of face region may be chosen for the newcollection. Eigenvectors may be re-sized using interpolation to thestandard size. The samples of different dimension may be analyzed usingdifferent standard sizes of face region.

The modified representation framework may be generated in accordancewith the following:

${\hat{C}{ov}_{C}} = {{\frac{N^{C\; 1}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 1} \times {\hat{V}}^{C\; 1} \times {\hat{E}}^{C\; 1^{T}}} \right\rbrack} + {\frac{1}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {\left( {S^{C\; 2} - {Mean}^{C\; 2}} \right) \times \left( {S^{C\; 2} - {Mean}^{C\; 2}} \right)^{T}} \right\rbrack} + {{\frac{N^{C\; 1}N^{C\; 2}}{\left( {N^{C\; 1} + N^{C\; 2}} \right)^{2}}\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack} \times \left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}}}$One or more storage media may be provided having embodied thereinprogram code for programming one or more processors to perform any ofthe methods described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the application of PCA to a raw dataset.

FIG. 2 illustrates the combining of two different PCA representations ofdatasets in accordance with a preferred embodiment.

FIG. 3 illustrates the combining of PCA representations of datasets withsupplemental raw data in accordance with a preferred embodiment.

FIG. 4 shows several plots of eigenvalue distributions for both a firstand a second collection for both the classical PCA method and a methodin accordance with a preferred embodiment.

FIGS. 5 a-5 d illustrate first eigenfaces from both a first and a secondcollection for both the classical method and a method in accordance witha preferred embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

PCA analysis is a very common technique used signal processing forreducing data dimensions and in pattern recognition for featureextraction. The main disadvantage of the technique is that the resultedPCA features are data dependent which means that they have to bere-computed every time the data collection changes its format due tomerging or splitting between multiple independent datasets oradding/deleting data samples from a given dataset. Embodiments of theinvention are described below for combining multiple PCA datasets.Embodiment are also provided for updating one PCA dataset when datasamples are changed using the old PCA values and the statisticalproperties of the PCA space of each dataset without using the originaldata values. This is very useful when the original data values are nolonger available or when is not practical to re-use them for very largedata collections.

Face recognition tasks are described for two cases. The first case iswhen it is desired to combine two face collections already analyzedusing PCA without applying PCA analysis on the merged face collection.The second case is when it is desired to add new face samples to onecollection already trained using PCA. The described methods are shown toyield at least similarly effective results as the classical approach ofapplying the PCA algorithm on the merged collection, while involving farless computational resources.

The techniques provided herein offer a significant saving incomputational effort and are quite robust and offer high repeatabilityin the context of eigenface analysis. The algorithm of re-computing thenew eigenspace is preferably similar to the approach described in HallP., Marshalland D., and Martin R. “Adding and Subtracting Eigenspaces”British Machine Vision Conference, Vol 2, 1999, pp: 463-472; and HallP., D. Marshall, and R. Martin. “Merging and splitting eigenspacemodels.” PAMI, 22(9), 2000, pp: 1042-1048, which are each herebyincorporated by reference. The data samples may be re-projected into thenew eigenspace without using the original data samples (the originalfaces), and instead using the old data projections (the old principalcomponents).

A formal theoretical explanation of this method is provided below, andit is demonstrated that it is be broadly applicable to otherapplications when PCA based analysis is employed. A theoretical basis ofprinciple component analysis as it is applied to eigenface analysis offace regions is next described. Preferred and alternative approaches tocombining training data from multiple, previously-trained, datasets arethen discussed. We next present the results of some experiments withimage collections drawn from very different sources and demonstrate thepractical results of applying our technique. Finally a description ofthe application of this technique in building practical tools and anapplication framework for the analysis, sorting and management ofpersonal image collections is given.

Theory

Principal Component Analysis (PCA) is one of the most common approachesused in signal processing to reduce the dimensionality of problems wherewe need to deal with large collections of data samples. PCA is a lineartransformation that maps the data to a new coordinate system so that thegreatest variance across the data set comes to lie on the firstcoordinate or principal component, the second greatest variance on thesecond coordinate, and so on. These basis vectors represent theeigenvectors of the covariance matrix of the data samples and thecoefficients for each data sample are the weights, or principalcomponents of that data sample. Unlike other linear transformations,such as DCT, PCA does not have a fixed set of basis vectors. Its basisvectors depend on the data set.

PCA can be used for reducing dimensionality in a dataset while retainingthose characteristics of the dataset that contribute most to itsvariance, by keeping lower-order principal components and ignoringhigher-order ones. One of the advantages of PCA is that we need onlycompare the first 20 principle components out of a possible 1028components where we use face regions of 32×32 pixel size. Calculatingthe distance between the principal components of two given data samplesallows a measure of similarity between the two samples to be determined.

The basis vectors for PCA are not fixed, thus when new data samples areadded to a data set there are issues as to the validity andapplicability of the PCA method. In particular, two situations which mayarise include the following:

-   -   (i) There are two collections of data which are already analyzed        using PCA and it is desired to determine a common basis vector        set for the combined collection and, ideally, transform the        predetermined PCA descriptors without having to recalculate new        descriptor sets for each item of data; and    -   (ii) There is an existing collection of data which is analyzed        using PCA and it is desired to add a significant number of new        raw data items to this dataset.

The classical solution for either of these cases is to recalculate thefull covariance matrix of the new (combined) dataset and thenrecalculate the eigenvectors for this new covariance matrix.Computationally, however, this is not an effective solution, especiallywhen dealing with large collections of data.

A different technique is provided herein to calculate the basis vectors,the eigenvalues and to determine the principle components for the newcollection. The first eigenvector and the first set of eigenvalues areused from each collection in case (i), and preferably only these. Thefirst eigenvector and the first set of eigenvalues from the originalcollection and the new data are used in case (ii). These have theadvantages that the original data samples need not be saved in memory,and instead only the principle components of these samples are stored.Also, the new set of eigenvectors are calculated from the eigenvectorsoriginally calculated for each collection of data. A detailedmathematical description of these techniques are provided below.

PCA Mathematical Model

To begin, assume a collection of N data samples S_(i) with i={1,N}. Eachdata sample is a vector of dimension m with m<N. The first step consistsin changing the collection of data so that it will have a zeros mean,which is done by subtracting the mean of the data samples(Mean_(S)=ΣS_(i)/N) from each sample. The PCA algorithm consists incomputing the covariance matrix Cov_(SS) using eq. 1:

$\begin{matrix}{{Cov}_{SS} = {{\frac{1}{N}\left\lbrack {S - {Mean}_{S}} \right\rbrack} \times \left\lbrack {S - {Mean}_{S}} \right\rbrack^{T}}} & (1)\end{matrix}$

The matrix S is formed by concatenating each data vector S_(i). The sizeof the covariance matrix is equal to m×m and is independent of thenumber of data samples N. We can compute the eigenvector matrix E=[e₁ e₂. . . e_(m)] where each eigenvector e_(i) has the same dimension as thedata samples m and the eigenvalues [v₁v₂ . . . v_(m)] of the covariancematrix using eq 2:Cov_(SS) =E×V×E ^(T)   (2)where the matrix V has all the eigenvalues on the diagonal and zeros inrest.

$\begin{matrix}{V = \begin{bmatrix}v_{1} & 0 & \ldots & 0 \\0 & {v2} & \ldots & 0 \\\vdots & \vdots & \vdots & \vdots \\0 & 0 & \ldots & {vm}\end{bmatrix}} & (3)\end{matrix}$

We can reconstruct each data samples using a linear combination of alleigenvectors using eq. 4.S _(i) =E×P _(i)+Mean_(S)   (4)where P_(i) represents the principal component coefficients for datasample S_(i) and can be computed by projecting the data sample on thecoordinates given by the eigenvectors using eq 5.P _(i) =E ^(T) ×[S _(i)−Mean_(S)]  (5)

By arranging the eigenvalues in descending order we can approximate thecovariance matrix by keeping only a small number of eigenvectorscorresponding to the largest values of the eigenvalues. The number ofeigenvalues is usually determined by applying a threshold to the values,or maintaining the energy of the original data. If we keep the first n<meigenvalues and their corresponding eigenvectors, the approximation ofthe covariance matrix can be computed as:Côv_(SS) =Ê×{circumflex over (V)}×Ê ^(T)   (6)with V=[v₁ v₂ . . . v_(n)]

The data can be as well approximated using only the first n principalcoefficients which correspond to the eigenvectors with largestvariations inside the data collection.Ŝ _(i) =Ê×P _(i)+Mean_(S)   (7)

The standard results of applying PCA to a raw dataset are illustrated inFIG. 1.

Dataset Combination Scenarios

Let's assume that we have one collection of data C¹ which is analyzedusing PCA algorithm which means we have its eigenvectors E^(C1)=[e^(C1)₁e^(C1) ₂ . . . e^(Cl) _(n1)], the eigenvalues [v^(C1) ₁v^(C1) ₂ . . .v^(Cl) _(n1)], the PCA coefficients for each sample in the collectionPc^(C1) and supplementary we also stored the mean data sample in thecollection Mean^(Cl). We also can assume at this moment that theoriginal data samples are no longer available for analysis or is notpractical viable to access them again. This fact is important whenworking with very large datasets where it will be time consuming tore-read all datasamples for applying classical PCA or when working withtemporary samples that can be deleted after they are first analyzed(e.g. when working with images for face recognition the user may deletesome used to construct PCA based models).

Now we consider two different cases where the data in the collectionwill be changed:

-   -   (i) either a new collection of data which was already analyzed        using PCA has to be added to the original collection in order to        form a super-collection, or    -   (ii) a new set of raw (unanalyzed) data samples are to be added        to the collection in order to update it.

Lets consider the first case of combination:

Combining Two Collections of PCA Data

Let's assume we want to combine collection C¹ described above withanother collection of data C² also PCA analyzed with eigenvectorsE^(C2)=[e^(C2) ₁e^(C2) ₂ . . . e^(C2) _(n2)], eigenvalues [v^(C2)₁v^(C2) ₂ . . . v^(C2) _(n2)], the PCA coefficients Pc^(C2) and the meandata sample Mean^(C2). We want to combine the two collections into asuper collection C without accessing the original data from the twocollections S^(C1) and S^(C2) (S^(C1) and S^(C2) are data matrices whereeach column S^(Ci) _(j) represented a vector data sample). The meansample in the collection can be computed as:

$\begin{matrix}{{Mean} = \frac{{N^{C\; 1}*{Mean}^{C\; 1}} + {N^{C\; 2}*{Mean}^{C\; 2}}}{N^{C\; 1} + N^{C\; 2}}} & (8)\end{matrix}$where N^(C1) and N^(C2) represent the number of data samples in eachcollection. It is easy to prove [5] that the covariance of the supercollection Cov_(C) can be computed as:

$\begin{matrix}{{Cov}_{C} = {{{\frac{1}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {\left( {S^{C\; 1} - {Mean}} \right)\left( {S^{C\; 2} - {Mean}} \right)} \right\rbrack} \times \left\lbrack {\left( {S^{C\; 1} - {Mean}} \right)\left( {S^{C\; 2} - {Mean}} \right)} \right\rbrack^{T}} = {{\frac{1}{N^{C\; 1} + N^{C\; 2}}\left\lbrack \left( {S^{C\; 1} - {Mean}^{C\; 1}} \right) \right\rbrack} \times {\left\lbrack \left( {S^{C\; 1} - {Mean}^{C\; 1}} \right) \right\rbrack^{T}++}\frac{1}{N^{C\; 1} + N^{C\; 2}}{\quad{{\left\lbrack \left( {S^{C\; 2} - {Mean}^{C\; 2}} \right) \right\rbrack \times {\left\lbrack \left( {S^{C\; 2} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}++}\frac{1}{N^{C\; 1} + N^{C\; 2}}{\frac{N^{C\; 1}N^{C\; 2}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack} \times \left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}} = {{\frac{N^{C\; 1}}{N^{C\; 1} + N^{C\; 2}}{Cov}_{C\; 1}} + {\frac{N^{C\; 2}}{N^{C\; 1} + N^{C\; 2}}{{Cov}_{C\; 2}++}\frac{N^{C\; 1}N^{C\; 2}}{\left( {N^{C\; 1} + N^{C\; 2}} \right)^{2}}{\quad{\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack \times \left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack}}}}}}}}} & (9)\end{matrix}$

As was stated above we cannot re-compute the covariance matrix using eq.2 which requires all of the original data samples, in our case theoriginal faces. There are two options: either we store the completecovariance matrices from the two collections and use them to compute theexact values of the covariance matrix of the supercollection or we canapproximate each covariance matrix using the eigenvalues andeigenvectors from each individual collection, viz:

$\begin{matrix}{{C\hat{o}v_{C}} = {{\frac{N^{C\; 1}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 1} \times {\hat{V}}^{C\; 1} \times {\hat{E}}^{C\; 1^{T}}} \right\rbrack} + {\frac{N^{C\; 2}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 2} \times {\hat{V}}^{C\; 2} \times {\hat{E}}^{C\; 2^{T}}} \right\rbrack} + {\frac{N^{C\; 1}N^{C\; 2}}{\left( {N^{C\; 1} + N^{C\; 2}} \right)^{2}}{\quad{\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack \times \left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}}}}}} & (10)\end{matrix}$

If we assumed that from each collection the eigen decomposition (numberof eigenvectors retained) was done so that the energy of the dataset isconserved we can assume (prove later in tests) that the face space givenby eigen-decomposition of the covariance matrix of the super collectionwill be close to the estimated face space given by theeigen-decomposition of the estimated covariance matrix given by eq. 9.

In other words we have to show that the estimated eigenvectors andeigenvalues using the covariance matrix computed in eq 9 are close tothe eigenvectors and eigenvalues computed applying classical PCA on theconcatenated supercollection. Not all eigenvectors will be similar, onlythe ones corresponding to the highest variations in the datasets (withthe largest corresponding eigenvalues).

The reconstruction of a combined dataset from two independently trainedPCA data representations is illustrated in FIG. 2.

Another issue that may need to be addressed is the case where the twocollections of data contain samples of different dimension. For example,in face recognition it might be necessary to combine two collections offaces that were analyzed using different standard sizes of face region.In this case we should choose a standard size of face region for thesuper collection (e.g. the minimum of the two sizes used), resizingusing interpolation the eigenvectors of the combined collection to thisstandard size

Once we have determined the covariance matrix of the super collection wecan use the eigen decomposition again and compute the eigenvectors E=[e₁e₂ . . . e_(n)] and the eigenvalues V=[v₁ v₂ . . . v_(n)] of the supercollection. The number of eigenvalues kept for analysis n is independentof n₁ and n₂. Once we have the eigenvectors we can project the datasamples. Remember that we don't have the original data samples toproject them easily so we have to re-create them from the old PCAcoefficients. If we want to re-create a data sample we can use eq. 4.The result represents the data sample from which the mean data sample incollection 1 was subtracted so the exact value of the data sample iscomputed as:Ŝ _(i) _({C1,C2}) =Ê ^({C1,C2}) ×P _(i) _({C1,C2}) +Mean^({C1,C2})  (11)

We have to subtract the mean of the super collection Mean (eq. 8) fromthis data sample. We can re estimate the Pc coefficients for each datasample in the super collection as:{circumflex over (P)}c _(i) ^({C1,C2}) =Ê ^(T) ×[E ^({C1,C2}) ×P _(i)^({C1,C2})+Mean^({C1,C2})−Mean]  (12)

In this case we assume that we have the collection of data C¹ describedand we want to add new N^(C2) data samples that are not analyzedalready. The sample matrix is S^(C2) and their mean value is Mean^(C2).The new covariance matrix will be computed as:

$\begin{matrix}{{\hat{C}{ov}_{C}} = {{{{\frac{N^{C\; 1}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 1} \times {\hat{V}}^{C\; 1} \times {\hat{E}}^{C\; 1^{T}}} \right\rbrack}++}{\frac{1}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {\left( {S^{C\; 2} - {Mean}^{C\; 2}} \right) \times \left( {S^{C\; 2} - {Mean}^{C\; 2}} \right)^{T}} \right\rbrack}} + {\frac{N^{C\; 1}N^{C\; 2}}{\left( {N^{C\; 1} + N^{C\; 2}} \right)^{2}}{\quad{\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack \times \left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}}}}}} & (13)\end{matrix}$

Applying the same algorithm as described in (1) we compute the neweigenvectors and eigenvalues. Using eq. 13 we can update the PCAcoefficients of the initial collection and to compute the PCAcoefficients of the new data samples we use:{circumflex over (P)}c _(i) ^(C2) =Ê ^(T) ×[S _(i) ^(C2)−Mean]  (14)where the Mean matrix can be computed using eq. 8.

This situation where additional raw data is added to a dataset with a(trained) PCA representation is illustrated in FIG. 3.

Experimental Results

We applied the method described in the previous section for our purpose:face recognition. We used an initial test collection of 560 faces (56individuals each with 10 faces). The images are separated randomly intotwo datasets: the training dataset containing half of the faces and theremaining half were used as a testing dataset.

Two separate tests were performed by splitting the training faces intotwo collections with different number of faces. The faces were randomlyattached to one of the initial collections:

-   -   1. Test A: we split the training collection into 2 collections        each with 140 faces and performed classification tasks using        three cases: simple concatenation of PCA coefficients without        updating, classical combination using data samples and the        proposed method.    -   2. Test B: using two collections one with 240 faces and the        other with the remaining 40 faces in two cases: the classical        approach and the proposed method. Also for this test we used        both scenarios: combining two collections of PCA data and adding        new data to a trained collection.

All faces were resized to 16×16 pixels, gray scale images were used andthe number of PCA coefficients used in the classification stage wasalways 20. For classification the nearest neighbourhood method waspreferred and the Euclidean distance between feature vectors was used.

FIG. 4 represents the variation of the first 50 eigenvalues using theclassical approach of combining two collections and the proposed methodalong with the eigenvalue variations inside the two separatecollections. It can be noticed that the variations between the classicalapproach of combining the method and the proposed approach are verysimilar close to identical in the first part of the graph where theclassical eigenvalues can not be noticed.

In order to see how the eigenvectors differ from the classicalcombination compared with the proposed method FIG. 2 shows the firsteigenfaces from each collection along with the first eigenfaces obtainedusing the classical combination and the proposed method. It can be notedthat the representation using the two methods have almost identicaldistributions.

It can be noted that the first eigenvector obtained applying theclassical PCA over the combined collection is similar with the firsteigenvector obtained using our approach and both of them are reallydifferent compared with the first eigenvector from each of the twosub-collections that we want to combine.

For Test A our second scenario is unlikely because the collections havethe same number of samples so we tested only the first scenario:combining the two collections. The results are given in the first table.

TABLE 1 Recognition Rates for Test A Combining collections Simpleconcatenation 48.32% Classical combination 84.28% Proposed method 85.23%

For Test B we used both scenarios: combining two collections (one having240 data samples and the other having only 40 samples) and adding newsample to one collection. The results are given in Table 2.

TABLE 2 Recognition Rates for Test B Combining Adding samplescollections to collection Simple concatenation 62.14% Na Classicalcombination 84.28% 84.28% Proposed method 84.64% 83.14%

It can be observed that in both tests the proposed combination methodhad the results very close to the classical approach of completelyre-analyzing the newly combined collection using PCA. On the other hand,as expected, if the PCA coefficients are not updated after combinationor the addition of multiple samples to the collection the recognitionrate drops significantly. For our test case, adding 16% of new images toa collection produced more than a 20% decline in the recognition rate.

Techniques have been described for updating the PCA coefficients of datasamples when the collection of data changes due to adding new data orcombining two collections of data previously analyzed using PCA into asuper collection. An advantage of the techniques is that they do notrequire that the original dataset is preserved in order to update itscoefficients. This is very helpful when analyzing large collections ofdata and mandatory when the original data is lost. Another advantage isthat the technique is much faster than the classical method orrecomputing of the PCA coefficients using the original dataset, becausethe dimension of the PCA data is significantly smaller than thedimension of the original data, and one of the properties of the PCAalgorithm is its dimensionality reduction. For example, if a face imageraw data sample has 64×64 pixels, about 5 k of pixel data is used instoring it in order to keep that data sample. Now, if there are 100faces, then 500 k of data space is involved. In a PCA representation,probably 20-30 basis vectors are used to describe each face. That meansthat 100 images can be stored using about 3000, or 3 k of data, which ismore than 130 times less than storing the raw data samples. So, anadvantage of the technique is that the original face images are notneeded as the technique regenerates them from the PCA representationframework.

While an exemplary drawings and specific embodiments of the presentinvention have been described and illustrated, it is to be understoodthat that the scope of the present invention is not to be limited to theparticular embodiments discussed. Thus, the embodiments shall beregarded as illustrative rather than restrictive, and it should beunderstood that variations may be made in those embodiments by workersskilled in the arts without departing from the scope of the presentinvention as set forth in the claims that follow and their structuraland functional equivalents.

In addition, in methods that may be performed according to the claimsbelow and/or preferred embodiments herein, the operations have beendescribed in selected typographical sequences. However, the sequenceshave been selected and so ordered for typographical convenience and arenot intended to imply any particular order for performing theoperations, unless a particular ordering is expressly provided orunderstood by those skilled in the art as being necessary.

All references cited above, as well as that which is described asbackground, the invention summary, the abstract, the brief descriptionof the drawings and the drawings, are hereby incorporated by referenceinto the detailed description of the preferred embodiments as disclosingalternative embodiments.

We claim:
 1. A consumer digital camera including a processor programmedby digital code to perform a face recognition method for working withtwo or more collections of facial images, wherein the method comprises:(a) determining distinct representation frameworks for first and secondsets of facial regions extracted from corresponding image collectionseach framework including at least principle component analysis (PCA)features; (b) storing representations of said first and second sets offacial regions using their respective representation frameworks; (c)determining a third, distinct representation framework based on therepresentations of the first and second sets of facial regions; (d)combining the stored representation of the first and the second sets offacial regions without using original facial image samples; includingback-projecting the sets of facial regions into their respectiverepresentation frameworks, combining the two back-projectedrepresentations of these sets of facial regions into a combined dataset,and forward projecting the combined dataset into the thirdrepresentation framework; (e) storing a representation of the combineddataset using said third representation framework; (f) comparing arepresentation of a current facial region, determined in terms of saidthird representation framework, with one or more representations offacial images of the combined dataset; and (g) based on the comparing,determining whether one or more of the facial images within the combineddataset matches the current facial image.
 2. The consumer digital cameraof claim 1, wherein the method further comprises updating the PCAfeatures based on first eigenvectors and first sets of eigenvalues foreach of the first and second sets of facial regions.
 3. The consumerdigital camera of claim 2, wherein the updating comprises calculating anew set of eigenvectors from the previously calculated firsteigenvectors of the first and second sets of facial regions.
 4. Theconsumer digital camera of claim 1, wherein the method does not useoriginal data samples of the first and second sets of facial regions. 5.The consumer digital camera of claim 1, wherein the first and secondsets of facial regions contain samples of different dimension, and themethod further comprises: (i) choosing a standard size of face region,and (ii) re-sizing eigenvectors using interpolation to the standardsize.
 6. The consumer digital camera of claim 5, wherein said samples ofdifferent dimension were analyzed using different standard sizes of faceregion.
 7. The consumer digital camera of claim 1, wherein the methodfurther comprises generating the third representation frameworkaccording to the following:${\hat{C}{ov}_{C}} = {{{{\frac{N^{C\; 1}}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {{\hat{E}}^{C\; 1} \times {\hat{V}}^{C\; 1} \times {\hat{E}}^{C\; 1^{T}}} \right\rbrack}++}{\frac{1}{N^{C\; 1} + N^{C\; 2}}\left\lbrack {\left( {S^{C\; 2} - {Mean}^{C\; 2}} \right) \times \left( {S^{C\; 2} - {Mean}^{C\; 2}} \right)^{T}} \right\rbrack}} + {\frac{N^{C\; 1}N^{C\; 2}}{\left( {N^{C\; 1} + N^{C\; 2}} \right)^{2}}{\quad{\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack \times {\left\lbrack \left( {{Mean}^{C\; 1} - {Mean}^{C\; 2}} \right) \right\rbrack^{T}.}}}}}$